Least Common Multiple (LCM) of 198 and 157
The least common multiple (LCM) of 198 and 157 is 31086.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 198 and 157?
First, calculate the GCD of 198 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 157 = 1 remainder 41 |
| 2 | 157 ÷ 41 = 3 remainder 34 |
| 3 | 41 ÷ 34 = 1 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 151 | 25821 |
| 184 and 163 | 29992 |
| 149 and 19 | 2831 |
| 141 and 176 | 24816 |
| 79 and 140 | 11060 |